Propensity score estimation: neural networks, support vector machines, decision trees (CART), and meta-classifiers as alternatives to logistic regression

Abstract

SummaryObjective-Propensity scores for the analysis of observational data are typically estimated using logistic regression. Our objective in this Review was to assess machine learning alternatives to logistic regression which may accomplish the same goals but with fewer assumptions or greater accuracy.Study Design and Setting-We identified alternative methods for propensity score estimation and/or classification from the public health, biostatistics, discrete mathematics, and computer science literature, and evaluated these algorithms for applicability to the problem of propensity score estimation, potential advantages over logistic regression, and ease of use.Results-We identified four techniques as alternatives to logistic regression: neural networks, support vector machines, decision trees (CART), and meta-classifiers (in particular, boosting).Conclusion-While the assumptions of logistic regression are well understood, those assumptions are frequently ignored. All four alternatives have advantages and disadvantages compared with logistic regression. Boosting (meta-classifiers) and to a lesser extent decision trees (particularly CART) appear to be most promising for use in the context of propensity score analysis, but extensive simulation studies are needed to establish their utility in practice.

Estimation and Inference of Heterogeneous Treatment Effects using Random Forests

“…Thus, if we knew e(x), we would have access to a simple unbiased estimator for τ (x); this observation lies at the heart of methods based on propensity weighting [e.g., Hirano et al, 2003]. Many early applications of machine learning to causal inference effectively reduce to estimating e(x) using, e.g., boosting, a neural network, or even random forests, and then transforming this into an estimate for τ (x) using (3) [e.g., McCaffrey et al, 2004, Westreich et al, 2010. In this paper, we take a more indirect approach: We show that, under regularity assumptions, causal forests can use the unconfoundedness assumption (2) to achieve consistency without needing to explicitly estimate the propensity e(x).…”

Stacked Generalization: An Introduction to Super Learning

“…31 Indeed, some researchers have been advocating for the use of data-adaptive methods, including the Super Learner, for effect estimation via singlyrobust methods, depending on estimation of either the conditional mean outcome or the propensity score. [21][22][23][24][25][26][27] While flexible algorithms can reduce the risk of bias due to regression model misspecification, a serious concern is that the use of data-adaptive algorithms in this context can result in invalid statistical inference (i.e. misleading confidence intervals).…”

Impact Assessment in Observational Studies: A Classification and Regression Tree Approach

“…Further, trees can handle a variety of input variable types as well as missing values. Finally, regression models require the assessment of the linearity assumption, which is typically overlooked (Westreich et al, 2010), whereas trees do not make this assumption.…”

“…Scholars have discussed the potential of this approach in epidemiological (Little and Rubin, 2000), sociological (Winship and Sobel, 2004), and econometric (Dehejja and Wahba, 2002;Heckman et al, 1997Heckman et al, , 1998 literature, and this method has also found promising applications in management and information systems research to assess causal effects at the individual and firm levels (e.g., Rubin and Waterman, 2006;Mithas and Almirall, 2006;Mithas et al, 2005;Mithas and Lucas, 2010). In almost all these applications, researchers use a logistic or a probit model to compute propensity scores, with a small emergent research (Lee et al, 2010;Westreich et al, 2010) on the use of classification trees and their variants for computing propensity scores instead of logistic regression.…”